Pharmacodynamic Study of AZD1722 in End-stage Renal Disease Patients on Hemodialysis: Complete Statistical Analysis

1. Trial at a Glance

This page covers the registry results for Pharmacodynamic Study of AZD1722 in End-stage Renal Disease Patients on Hemodialysis (NCT01764854), a randomized phase 2 study. The primary outcome is Change in Mean Weekly Interdialytic Weight Gain (IDWG).

2. Clinical Question

3. Trial Design

This was a Phase 2a, randomized, double-blind, placebo-controlled study with a parallel design. The masking field records quadruple masking. The study is marked completed, with enrollment recorded as 88. The sponsor was Ardelyx. The registry lists a start date of 2013-01 and primary completion in 2013-10.

Four groups are described: AZD1722 and placebo in inpatient arms, and AZD1722 and placebo in outpatient arms. The inpatient AZD1722 arm is described as tenapanor administered in a clinical pharmacology unit. The inpatient placebo was described as size- and color-matched to the experimental drug and administered in that unit. The outpatient arms were AZD1722 and placebo. The primary endpoint description explicitly restricts the analysis to the outpatient groups because the inpatient groups were treated for one week.

The reported arm summaries for the primary endpoint include 37 participants in the outpatient AZD1722 arm and 35 in the outpatient placebo arm. These are the arm counts for that outcome, not a replacement for the overall enrollment figure. The registry record does not report the randomization method, allocation concealment procedures, treatment doses, or a detailed schedule of visits beyond the stated run-in and Week 4 endpoint timeframe. The study also lists stool sodium content as a secondary outcome. A total of 2 outcome measures and 2 analyses are recorded, while one secondary outcome is posted.

4. Participant Flow and Accounting

The registry reports how participants moved through each stage of the study. All counts below are exactly as posted; missing counts are not inferred from other stages.

Overall Study

Reasons for not completing this period:

Analysis population for the primary outcome, as defined in the registry: The out-patient arms were the only groups that were pre-specified to be included in this analysis since the in-patient arms were only treated for one week.

5. Baseline Characteristics

The table reproduces the baseline characteristics posted in the registry, which describe the participants analysed at baseline and help show whether the randomized groups were comparable.

6. Primary Endpoint

The registry lists the primary outcome as Change in Mean Weekly Interdialytic Weight Gain (IDWG), measured over Run-in period (Weeks -2 and -1) versus Week 4 (end of treatment).

The primary endpoint is change in mean weekly interdialytic weight gain (IDWG), measured in kilograms. The record says that participants were weighed before dialysis prior to their first dialysis of the week. The measure tracks change in pre-dialysis weight over time, comparing the run-in period in Weeks -2 and -1 with Week 4, the end of treatment.

IDWG is relevant to the study question because it describes weight change between dialysis sessions. In general, a continuous endpoint preserves the size of observed changes on its measurement scale, rather than reducing them to a yes-or-no outcome. The registry describes the endpoint as a mean, with standard deviation as its measure of spread. That allows the group summaries to show both the average change and the variability among participants.

The reported outpatient mean changes were -0.26 kilograms for AZD1722 and -0.23 kilograms for placebo. These are group-level summaries. They do not, on their own, show how individual participants changed or establish why a change occurred. The primary endpoint description identifies the outpatient groups as the analysis population because the inpatient groups received treatment for one week. Details about how the weekly measurements were combined or how missing weights were handled are not reported in the registry record.

7. Results Posted in the Registry

• AZD1722 Out-patient: mean -0.26 versus -0.23 on control; difference -0.03 (95% CI -0.45 to 0.39), standardized effect d = -0.03; z-test p = 0.888.

8. Statistical Interpretation

9. Statistical Methods Explained

Statistical methods are easiest to interpret by keeping the reported sponsor analysis separate from the simple recalculation based on group summaries. The registry gives a sponsor-reported ANCOVA p-value of 0.46. The recalculated unadjusted comparison uses the outpatient arm means and standard deviations and reports a mean difference of -0.03 kilograms, a confidence interval, and an unadjusted p-value of 0.888. These figures answer related but not identical statistical questions: ANCOVA can incorporate covariates, while the recalculation is an unadjusted comparison of the posted summaries. The registry does not report which covariates were included in ANCOVA.

What does a mean difference represent?

For a continuous outcome, the mean summarizes the average value in a group. A mean difference contrasts the two group means on the original measurement scale. Here, the posted means are -0.26 kilograms for AZD1722 and -0.23 kilograms for placebo, and the recalculated difference is -0.03 kilograms. The sign depends on the stated subtraction order; the recalculation uses AZD1722 minus placebo. The difference is an estimate from these study groups, not a guarantee of the exact contrast in a larger population.

Why report standard deviations?

A standard deviation describes how dispersed individual observations are around a group mean. The registry reports standard deviations of 0.939 kilograms in the outpatient AZD1722 arm and 0.871 kilograms in the outpatient placebo arm. In general, a mean alone does not show whether observations cluster closely around the average or vary widely. The standard deviations help describe that variation, but do not reveal the shape of the outcome distribution or individual participant trajectories. The registry does not report those distributions.

What is a confidence interval?

In general, a confidence interval expresses uncertainty about an estimated quantity under a statistical procedure and its assumptions. The recalculated interval for the mean difference reaches across zero, which corresponds to no difference on that scale, and includes values on both sides. It therefore does not narrowly determine the direction of the unadjusted contrast. A confidence interval is not a range containing a fixed proportion of individual outcomes, nor does it assign a probability to the true value after the data have been observed.

How does ANCOVA differ from the recalculation?

In general, ANCOVA compares groups while adjusting for one or more covariates in a statistical model. Adjustment may change the estimated contrast and its uncertainty relative to a simple comparison of group summaries. The record reports the method name and p-value but does not report the covariates, model specification, adjusted estimate, standard error, or confidence interval. Those omissions prevent a detailed reconstruction or assessment of the sponsor model from the registry record alone.

What does randomization contribute?

In general, random assignment aims to make treatment groups comparable with respect to measured and unmeasured characteristics, on average, before treatment. It supports causal comparisons when the allocation process is implemented as intended and the analysis appropriately follows the design. The registry identifies the study as randomized but does not report the sequence-generation or concealment procedures. Masking is recorded as quadruple, and the study is described as double-blind in its official title; the record does not explain the roles covered by quadruple masking.

Why can variability matter for interpretation?

General statistical principle: when observations vary substantially relative to the effect being estimated, the estimate is less precise unless the study has enough information to offset that variability. The posted standard deviations are larger than the absolute value of the recalculated mean difference. This comparison describes the scale of the reported summaries; it does not by itself determine a study's power or clinical relevance. The registry record does not report an original sample-size justification or the assumptions used to design the trial.

The sample-size illustrations use the observed effect as a starting point and consider specified fractions of that effect. They are planning illustrations, not evidence about the probability that the trial detected an effect. Their assumptions and interpretation are described separately. Neither those illustrations nor the unadjusted recalculation should be confused with the sponsor's ANCOVA analysis.

10. Confidence Intervals and Precision

The recalculated unadjusted mean difference is -0.03 kilograms. Its confidence interval extends from a negative value to a positive value, crossing zero. This is important because the interval remains compatible with no difference and with contrasts in either direction under the recalculation's assumptions. The registry record reports the confidence limits to more decimal places than are appropriate to reproduce under the site's display convention, so the limits are not repeated.

In general, precision concerns how narrowly an estimate is bounded by its uncertainty interval. A narrow interval would constrain the range of values compatible with the data and method more closely; a broad interval leaves more uncertainty about the contrast's size and direction. The interval in this comparison does not provide a tightly determined estimate around the observed mean difference. Its inclusion of zero should not be interpreted as proof that the groups are identical.

The reported arm standard deviations, 0.939 kilograms for AZD1722 and 0.871 kilograms for placebo, describe dispersion in the continuous outcome. They provide context for the mean difference but are not themselves measures of uncertainty in that difference. The recalculated interval reflects uncertainty in the group contrast, while the sponsor ANCOVA p-value comes from a separate model whose estimate and interval are not reported.

Precision is also conditional on the analysis population and assumptions. The primary outcome analysis was specified for the outpatient groups. The registry record does not report how missing measurements, protocol deviations, or other departures from the intended analysis were handled. These reporting gaps limit a fuller evaluation of the uncertainty around the result.

11. Planning a Similar Trial: Sample Size

This is a planning illustration, not a re-evaluation of the original trial. It asks: if a new study wanted to detect a difference like the one observed, or a smaller one, how large would it need to be? It is deliberately not “observed power” of the finished trial, which is not a meaningful quantity.

The sample-size figures are planning illustrations based on the observed effect, not the original design calculation for this trial. The registry record does not report the assumptions used for the trial's own sample-size design. The illustrations assume a two-sided significance level of 0.05, equal allocation between the two arms, and a normal approximation. They consider detecting the stated fractions of the observed effect.

For the continuous-outcome comparison in this study, the figures are participants per arm, not a total across both arms and not total events. The row for 100% of the observed effect lists 14,337 participants per arm for 80% power and 19,193 participants per arm for 90% power. Planning for 75% of the observed effect lists 25,487 participants per arm for 80% power and 34,120 participants per arm for 90% power. Planning for 50% of the observed effect lists 57,345 participants per arm for 80% power and 76,769 participants per arm for 90% power.

In plain language, the 80% power column gives the illustrated number of participants per arm for a design with an 80% chance of detecting the specified effect if that effect is real and the planning assumptions hold. The 90% column makes the analogous illustration for a 90% chance. Smaller effects need more participants to detect under the same assumptions, as reflected in the rows that use smaller fractions of the observed effect. The associated curve is a visual illustration of this planning relationship, not an observed trial result. These figures are not observed power.

12. How the Sample Size Is Derived

Power is the probability that a study of a given size rejects the null hypothesis when a specific true effect exists. It depends on four things: the effect to detect, the variability of the outcome, the significance level (here a two-sided α of 0.05, so z_1−α/2 = 1.960) and the desired power (z_1−β = 0.842 for 80% and 1.282 for 90%).

Formula

n is the number of participants in each arm, Δ is the difference in means to detect and σ is the common standard deviation.

Worked calculation for this trial

1. Observed difference Δ = -0.030; pooled standard deviation σ = 0.907.
2. n = 2 × (1.96 + 0.842)² × 0.907² / -0.030² = 14,336.2, rounded up to 14,337 participants per arm for 80% power.

The smaller-effect rows in the table above repeat the same calculation with the effect multiplied by 0.75 and 0.5 (for ratios, applied to the logarithm of the ratio).

R code

alpha <- 0.05
z_a   <- qnorm(1 - alpha / 2)          # two-sided
delta <- -0.03                      # observed difference in means
sigma <- 0.906608672865137                     # pooled standard deviation
n_per_arm <- function(power, frac = 1) {
  ceiling(round(2 * (z_a + qnorm(power))^2 * sigma^2 / (delta * frac)^2, 6))
}
for (f in c(1, 0.75, 0.5))
  cat(sprintf("%3.0f%% of observed effect: n per arm = %s (80%% power), %s (90%% power)\n", 100 * f,
              format(n_per_arm(0.80, f), big.mark = ","), format(n_per_arm(0.90, f), big.mark = ",")))

# Check against R's built-in function (t-based, so very slightly larger)
cat("power.t.test:", round(power.t.test(delta = delta, sd = sigma, power = 0.80)$n, 1), "\n")

# Simulation: exact two-sample t-test using simulated means and variances
set.seed(1764854)
n    <- n_per_arm(0.80)
reps <- 20000
m_diff <- rnorm(reps, delta, sigma * sqrt(2 / n))             # difference in sample means
s2     <- sigma^2 * rchisq(reps, 2 * (n - 1)) / (2 * (n - 1))   # pooled sample variance
tstat  <- m_diff / sqrt(s2 * 2 / n)
cat(sprintf("Simulated power at n = %s per arm: %.3f (%d replicates)\n", format(n, big.mark = ","), mean(abs(tstat) > qt(0.975, 2 * (n - 1))), reps))

Output from running the code

100% of observed effect: n per arm = 14,337 (80% power), 19,193 (90% power)
 75% of observed effect: n per arm = 25,487 (80% power), 34,120 (90% power)
 50% of observed effect: n per arm = 57,345 (80% power), 76,769 (90% power)
power.t.test: 14337.2 
Simulated power at n = 14,337 per arm: 0.801 (20000 replicates)

The simulation draws many sets of group means and variances at the planned sample size and counts how often the two-sample t-test rejects the null. It should land close to the target power; at very small required sample sizes it can fall below it, because the normal approximation is rough there.

13. Analyses Reported by the Sponsor

The registry's sponsor-reported analysis is an ANCOVA comparison of the outpatient AZD1722 and placebo groups, with p = 0.46. The registry does not report the adjusted contrast, its confidence interval, or the covariates and other model details, so the full ANCOVA result cannot be reconstructed from the record.

The recalculated unadjusted comparison uses the posted group summaries. It reports a mean difference of -0.03 kilograms, a confidence interval spanning zero, and an unadjusted p-value of 0.888. This calculation does not reproduce ANCOVA and should not be presented as the sponsor's analysis. Adjustment for covariates can yield a different estimate or uncertainty from an unadjusted comparison, and the necessary model details are not reported in the registry record.

The record does not flag a discrepancy between the reported analysis and the recalculation. The sponsor's p-value and the recalculated summary-statistic result should therefore be read as outputs of different methods, not as interchangeable numbers. The sponsor result reflects the analysis identified in the registry; the recalculation offers a transparent, unadjusted comparison of the posted summaries.

14. Multiplicity, Missing Data and Analysis Populations

The registry records 2 outcome measures and 2 analyses, and one secondary outcome is posted: stool sodium content. The primary outcome is change in mean weekly IDWG. The record does not report whether, or how, the analysis accounted for testing multiple outcomes, time points, or comparisons. A multiplicity adjustment or a prespecified hierarchy is not reported in the registry record.

In general, making multiple statistical comparisons can increase the chance of at least one apparently unusual result, even when no true effects exist. Methods such as adjusting significance thresholds or specifying a testing hierarchy can address that issue, but the record does not say whether either approach was used. No adjustment should be assumed from the reported p-values alone.

The primary outcome description identifies the outpatient groups as the analysis population because inpatient treatment lasted one week. The posted arm summaries for the primary comparison are for the outpatient groups. The registry does not give a detailed definition of the analysis population, such as whether participants were analyzed according to randomized assignment or whether eligibility for the endpoint required a particular measurement.

Handling of missing data is also not reported in the registry record. The record does not describe the amount or pattern of missing endpoint measurements, any imputation method, or whether analyses were restricted to observed measurements. It also does not report sensitivity analyses examining the effect of missing data. These details matter because conclusions from a continuous endpoint can depend on how incomplete measurements are treated.

The registry does not report an interim-analysis plan, stopping rules, a detailed statistical analysis plan, or the original sample-size justification. Their absence from the registry record does not establish that such procedures were absent; it means their details cannot be assessed from this record.

15. Safety Results

The registry reports serious adverse events as affected participants divided by participants at risk.

Deaths

Other (non-serious) adverse events

Participants with at least one non-serious event at or above the registry's 5% reporting threshold.

Most frequent serious adverse event terms

Most frequent non-serious adverse event terms

Serious events with the highest arm-level rate: syncope (12.5%), acute respiratory failure (12.5%), local swelling (12.5%), pneumonia (2.9%), urinary tract infection (2.7%).

The safety figures are counts of participants affected in each arm, with the number at risk shown alongside them. For serious adverse events, the outpatient AZD1722 group had 2 affected participants among 37 at risk, and the outpatient placebo group had 1 among 35 at risk. In the inpatient arms, 0 of 8 AZD1722 participants and 3 of 8 placebo participants were reported as affected. The record lists 0 deaths in each of the four groups.

For other adverse events, 3 of 37 outpatient AZD1722 participants and 21 of 35 outpatient placebo participants were affected. In the inpatient groups, the corresponding counts were 6 of 8 and 2 of 8. These counts are descriptive; they do not by themselves establish that treatment caused an event or that differences between groups are statistically reliable. No safety comparison model or uncertainty interval is reported.

The registry lists serious-event terms with percentages: Syncope, acute respiratory failure, and local swelling each at 12.5%; pneumonia at 2.9%; and Urinary Tract Infection at 2.7%. The term list does not provide a full breakdown by group in the posted summary. Interpret the percentages as registry-reported figures rather than as a basis for comparing risks across arms. The registry record does not report additional detail about event timing, severity grading, or causal attribution.

16. What the Result Does, and Does Not, Mean

The posted outpatient summaries show mean weekly IDWG changes of -0.26 kilograms for AZD1722 and -0.23 kilograms for placebo. The recalculated unadjusted contrast is -0.03 kilograms, and its confidence interval crosses zero. The sponsor-reported ANCOVA p-value is 0.46. These results describe the recorded endpoint and its analysis; they do not determine whether AZD1722 produces a clinically important effect.

The interval's span across zero means the unadjusted data do not tightly resolve the direction of the contrast. That is not proof of no effect or proof of equivalence. Establishing equivalence would require an appropriate design and a prespecified margin, neither of which is reported in the registry record. Likewise, a p-value alone does not convey clinical importance or the likely range of effects.

The endpoint is a measure of weight change between dialysis sessions, not a direct measure of every aspect of fluid status or patient experience. The registry describes the study's purpose as assessing safety, tolerability, and activity related to fluid overload or weight gain. The primary analysis concerns the specified outpatient endpoint, and should not be generalized automatically to the inpatient groups, other populations, or other outcomes.

The safety counts provide a descriptive account of participants affected by serious and other adverse events, and the registry lists no deaths in the groups. They do not establish comparative safety on their own. The record does not give the detail needed to interpret event timing, attribution, or all possible differences in exposure and follow-up.

Overall, the results are best read as estimates with uncertainty from a randomized, placebo-controlled study, alongside important reporting limits. They do not establish a definitive benefit, lack of benefit, or safety conclusion. Further interpretation depends on the full analysis methods, completeness of endpoint data, and clinical context, details that are not reported in the registry record.

17. Why This Trial Matters Statistically

This study illustrates why the estimate, its uncertainty, and the analysis method need to be read together. The outpatient mean changes are close on the kilogram scale, while the recalculated confidence interval spans zero and reaches values in both directions. Reporting only a p-value would conceal the range of contrasts compatible with the unadjusted summary data. Conversely, focusing only on the observed difference would give too little attention to uncertainty.

The record also demonstrates that a sponsor-reported model and a simple recalculation are not interchangeable. ANCOVA can adjust for covariates, but the covariates and adjusted estimate are not reported. The unadjusted comparison is easier to reproduce from the group summaries, but it answers a narrower question. Clear reporting of both estimates, uncertainty intervals, and model specifications helps readers understand how conclusions depend on analytic choices.

Outcome population matters as well. The primary analysis was specified for outpatient arms because inpatient participants were treated for one week. Interpreting the outpatient result as if it summarized all study groups would ignore that design distinction. The different treatment settings and the separation of inpatient and outpatient arms are essential context for understanding which comparison the primary endpoint represents.

Finally, the planning illustration shows how assumptions about the target effect shape participant requirements. It is not a retrospective measure of whether the trial was adequately powered, and it is not observed power. The original design assumptions are not reported in the registry record. Together, these features make the study a useful example of careful separation between observed summaries, model-based analysis, planning calculations, and the limits of registry reporting.

18. Limitations

• The posted summary statistics are the only data these results rest on; patient-level data, full protocols and statistical analysis plans are not available.
• Recalculated results are simple, unadjusted calculations from posted summaries. They do not replace the sponsor's prespecified analysis.

The registry record gives limited detail about the primary analysis. It reports an ANCOVA method and p-value, but not the covariates, adjusted estimate, confidence interval, or model specification. This prevents readers from assessing how adjustment affected the comparison or reproducing the sponsor analysis. The unadjusted recalculation is not a substitute for those missing details.

The primary endpoint analysis was specified for outpatient arms only because the inpatient arms received treatment for one week. The primary comparison therefore does not summarize all four groups. The record also does not provide detailed information on how endpoint measurements were collected beyond the stated pre-dialysis weighing schedule and the run-in-to-Week 4 comparison.

Missing endpoint data, analysis-population definitions, protocol deviations, and sensitivity analyses are not reported in the registry record. The original sample-size justification, interim-analysis procedures, and any multiplicity approach are also not reported. These omissions constrain assessment of the planned analysis and the robustness of the findings.

Safety reporting is limited in the posted summary. Counts of affected participants and a list of serious-event terms are available, but event timing, attribution, severity details, and a full event-by-group breakdown are not reported. The registry record also does not provide a detailed account of treatment exposure or follow-up for interpreting safety counts.

These reporting limitations do not show that procedures or information were absent from the study; they limit what can be concluded from the registry record. Interpretation should remain tied to the endpoint, groups, analyses, and level of detail that are recorded.

19. Related Tutorials

20. Related Statistical Calculators

21. Sources

• ClinicalTrials.gov: Pharmacodynamic Study of AZD1722 in End-stage Renal Disease Patients on Hemodialysis — NCT01764854.
• Registry record last updated 2020-08-10; status last verified 2020-08.
• Results first posted 2020-08-10.
• Data retrieved from ClinicalTrials.gov on 2026-11-09.
• Group sizes, means, event counts and sponsor-reported p-values are reproduced as posted. Effect estimates, confidence intervals and p-values not attributed to the sponsor are independently calculated from the posted summary statistics.

22. Record Summary

The registry describes a completed randomized, double-blind, placebo-controlled, parallel Phase 2a study sponsored by Ardelyx. Enrollment is recorded as 88. The study included inpatient and outpatient AZD1722 and placebo arms and lists quadruple masking. Its primary endpoint was change in mean weekly IDWG from the run-in period in Weeks -2 and -1 to Week 4.

The primary analysis was specified for the outpatient groups. Their reported mean changes were -0.26 kilograms for AZD1722 and -0.23 kilograms for placebo. The recalculated unadjusted mean difference was -0.03 kilograms, with a confidence interval spanning zero; the sponsor-reported ANCOVA p-value was 0.46. The record also lists stool sodium content as a secondary outcome and reports safety counts by arm. Important analysis details, including missing-data handling and ANCOVA model specification, are not reported in the registry record.